If I have something like the following can I use the add inference rule to add ~A. Does that cause a contradiction, or am I fine since it's if A and not A being directly declared?

1. (A ⊃ B) ⊃ C 
2. ~D ⊃ B             

3.suppose ~D
4. B            2,3 MP
5. B v ~A       2 Add
6. ~A v B       5 Comm
7. A ⊃ B        6 CE
8. C            1,7 MP
Close supposition
9. ~D ⊃ C